Semi-classical orthogonal polynomials and the Painlevé equations

来源 :International Conference on Orthogonal Polynomials,Integrabl | 被引量 : 0次 | 上传用户:jzlh6890
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In this talk I shall discuss the relationship between the Painlevé equations and orthogonal polynomials with respect to semi-classical weights.It is well-known that orthogonal polynomials satisfy a threeterm recurrence relation.I will show that for some semi-classical weights,the coefficients in the recurrence relation can be expressed in terms of Wronskians that arise in the description of special function solutions of a Painlevé equation.The orthogonal polynomials discussed will include semiclassical Laguerre and Hermite weights and semi-classical generalizations of the Charlier and Meixner polynomials,which are discrete orthogonal polynomials.
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